An efficient shooting algorithm for Evans function calculations in large systems

In Evans function computations of the spectra of asymptotically constant-coefficient linear operators, a basic issue is the efficient and numerically stable computation of subspaces evolving according to the associated eigenvalue ODE. For small systems, a fast, shooting algorithm may be obtained by representing subspaces as single exterior products \cite{AS,Br.1,Br.2,BrZ,BDG}. For large systems, however, the dimension of the exterior-product space quickly becomes prohibitive, growing as $\binom{n}{k}$, where $n$ is the dimension of the system written as a first-order ODE and $k$ (typically $\sim n/2$) is the dimension of the subspace. We resolve this difficulty by the introduction of a simple polar coordinate algorithm representing ``pure'' (monomial) products as scalar multiples of orthonormal bases, for which the angular equation is a numerically optimized version of the continuous orthogonalization method of Drury--Davey \cite{Da,Dr} and the radial equation is evaluable by quadrature. Notably, the polar-coordinate method preserves the important property of analyticity with respect to parameters.Comment: 21 pp., two figure

Learning with multiple representations: An example of a revision lesson in mechanics

We describe an example of learning with multiple representations in an A-level revision lesson on mechanics. The context of the problem involved the motion of a ball thrown vertically upwards in air and studying how the associated physical quantities changed during its flight. Different groups of students were assigned to look at the ball's motion using various representations: motion diagrams, vector diagrams, free-body diagrams, verbal description, equations and graphs, drawn against time as well as against displacement. Overall, feedback from students about the lesson was positive. We further discuss the benefits of using computer simulation to support and extend student learning.Comment: 10 pages, 5 figures, 2 tables http://iopscience.iop.org/0031-912

Model-Independent Reionization Observables in the CMB

We represent the reionization history of the universe as a free function in redshift and study the potential for its extraction from CMB polarization spectra. From a principal component analysis, we show that the ionization history information is contained in 5 modes, resembling low-order Fourier modes in redshift space. The amplitude of these modes represent a compact description of the observable properties of reionization in the CMB, easily predicted given a model for the ionization fraction. Measurement of these modes can ultimately constrain the total optical depth, or equivalently the initial amplitude of fluctuations to the 1% level regardless of the true model for reionization.Comment: 4 pages, 5 figures, submitted to PRD (rapid communications

Fluorescence lifetime endoscopy using TCSPC for the measurement of FRET in live cells

Development of remote imaging for diagnostic purposes has progressed dramatically since endoscopy began in the 1960’s. The recent advent of a clinically licensed intensity-based fluorescence micro-endoscopic instrument has offered the prospect of real-time cellular resolution imaging. However, interrogating protein-protein interactions deep inside living tissue requires precise fluorescence lifetime measurements to derive the Förster resonance energy transfer between two tagged fluorescent markers. We developed a new instrument combining remote fiber endoscopic cellular-resolution imaging with TCSPC-FLIM technology to interrogate and discriminate mixed fluorochrome labeled beads and expressible GFP/TagRFP tags within live cells. Endoscopic-FLIM (e-FLIM) data was validated by comparison with data acquired via conventional FLIM and e-FLIM was found to be accurate for both bright bead and dim live cell samples. The fiber based micro-endoscope allowed remote imaging of 4 µm and 10 µm beads within a thick Matrigel matrix with confident fluorophore discrimination using lifetime information. More importantly, this new technique enabled us to reliably measure protein-protein interactions in live cells embedded in a 3D matrix, as demonstrated by the dimerization of the fluorescent protein-tagged membrane receptor CXCR4. This cell-based application successfully demonstrated the suitability and great potential of this new technique for in vivo pre-clinical biomedical and possibly human clinical applications

Perceptions and Barriers of Survivorship Care in Asia: Perceptions From Asian Breast Cancer Survivors.

PurposeWith the long-term goal to optimize post-treatment cancer care in Asia, we conducted a qualitative study to gather in-depth descriptions from multiethnic Asian breast cancer survivors on their perceptions and experiences of cancer survivorship and their perceived barriers to post-treatment follow-up.MethodsTwenty-four breast cancer survivors in Singapore participated in six structured focus group discussions. The focus group discussions were voice recorded, transcribed verbatim, and analyzed by thematic analysis.ResultsBreast cancer survivors were unfamiliar with and disliked the term "survivorship," because it implies that survivors had undergone hardship during their treatment. Cognitive impairment and peripheral neuropathy were physical symptoms that bothered survivors the most, and many indicated that they experienced emotional distress during survivorship, for which they turned to religion and peers as coping strategies. Survivors indicated lack of consultation time and fear of unplanned hospitalization as main barriers to optimal survivorship care. Furthermore, survivors indicated that they preferred receipt of survivorship care at the specialty cancer center.ConclusionBudding survivorship programs in Asia must take survivor perspectives into consideration to ensure that survivorship care is fully optimized within the community

Characterizing Invasiveness through a Descriptive Study of Guinea Grass (\u3ci\u3eMegathyrsus maximus\u3c/i\u3e) Growing in Three Habitat Types and Differing Herbivore Assemblages in Both Kenya and Texas

Guinea grass (Megathyrsus maximus syn. Panicum maximum) is an important pasture grass that has been introduced pantropically, yet in many cases has escaped cultivation and is invading native rangelands – threatening biodiversity at multiple trophic levels. An increasing challenge of rangeland management is balancing the importance of pasture grasses with their negative impact on ecosystem processes. Given this challenge, it is critical to understand the mechanisms that underlie grass invasion. In this descriptive study, our objective was to assess the ecological stress release hypothesis by comparing the relative abundance and functional traits of Guinea grass in Kenya\u27s home range with its introduced range in Texas, USA. To characterize Guinea grass dominance in Texas vs. Kenya, we measured plant height and cover and examined the associated arthropod and ungulate abundances. We characterized these associations across three habitat types of differing resource availability; 1) Under woody legumes with higher soil moisture and soil nitrogen, 2) grasslands with higher light yet drier soils, 3) riparian areas with higher soil water moisture and light. We found that Texas Guinea grass was 50% taller than Kenyan Guinea grass except for riparian environments comparable to its introduced range. Texan Guinea grass occupied 50% more area than Kenyan Guinea grass and was especially abundant under woody legumes. Texas ungulate communities were less diverse and abundant. The arthropod herbivore diversity was twice as high on Kenyan Guinea grass. These results suggest that Guinea grass has escaped a rich assemblage of herbivores and likely explains some of its spread in nonnative ranges. The interaction between resource environment and herbivory may elucidate mechanisms important for Guinea grass escaping cultivation in its introduced range and lays the foundation for future ecological studies and a search for biological control